Welcome to TeX.sx! On this site, a question should typically revolve around an abstract issue (e.g. "How do I get a double horizontal line in a table?") rather than a concrete application (e.g. "How do I make this table?"). Questions that look like "Please do this complicated thing for me" tend to get closed because they are "too localized". Please try to make your question clear and simple by giving a minimal working example (MWE): you'll stand a greater chance of getting help.
–
lockstepOct 17 '12 at 14:39

Which part are you stuck on? There are only a few things to deal with here: 1. Define the points with \coordinate (A1) at (<x>,<y>);. 2. Label the nodes: \node at (A1) {$A_1$};. 3. Draw the lines: \draw (A1) -- (A2), etc. all within a \begin{tikzpicture}...\end{tikzpicture}. The only part left that does require work is the shading and you can use the intersections library to help with that.
–
Peter GrillOct 17 '12 at 16:38

Once you get the basic structure, then you can use a \foreach loop to allow you to have one reusable diagram where you can just specify the number of vertices you want and the rest gets computed automatically. But first you need to do the manual diagram to be able to get started.
–
Peter GrillOct 17 '12 at 16:39

@lockstep: I feel that it is a problem that you and other high end users urge others not to post 'do this for me' questions - without any real power behind. Someone always do the work, and thereby encourage this behavior. -this is obviously not your fault, but maybe you can do something about the problem!? vote to close the question?
–
Hans-Peter E. KristiansenOct 18 '12 at 5:13

I've got the following message "This version uses the pst-xkey package for managing parameters Please read the doc, some macros have a new syntax use option old for upward compatibility c:/texlive/2012/texmf-dist/tex/generic/xkeyval/pst-xkey.tex". But afer 30sec the diagrams were drawn.
–
Américo TavaresOct 17 '12 at 20:55

Wow, I just got a down vote. Thanks!
–
kiss my armpitJan 3 '13 at 8:52

It will benefit you more if you read the pgf manual, especially if you have to draw more of these figures in the future. The manual gives detailed examples on how to use tikz to draw your LaTeX figures.

We will use your first figure in this demonstration. We can assign coordinates by using the \coordinate command. We can automate the assigning of coordinates but we shall not do that for the vertices of the polygon. We can type something like the following for the first three vertices:

For this type of diagram you really need to consider what the goal is. How much flexibility do you want to have:

Are those all the diagrams of this kind that you want drawn?

Do you want to be able to chose the line styles of each edge?

How do you want to specify which regions are shaded?

Questions like this will have an effect on the final solution. But before you can even begin to think about adding flexibility you need to be able to draw one of them. Here I have used fixed points so that this is easier to follow, but once you understand how this works, you can come up with an algorithm to automate this further perhaps generating the locations of the points.

Define the points:

Best to first define all the coordinates we need using the \coordinate (<node_name>)at (<x>,<y>) syntax so that we can easily makes changes later if needed.

\coordinate (A1) at (0,4);
\coordinate (A2) at (3,6);
...

Label the nodes:

To label the points we place a node at each vertex:

\node [left ] at (A1) {$A_1$};
\node [above] at (A2) {$A_2$};
...

Hmm, this seems a bit tedious to list out all the points. The only thing different between each node, is where it is placed relative to the point and the label. So, we can use a \foreach to simplify things:

As was pointed out in the comments, the included images had a combination dashed/dotted line. You could define a custom style for that (which would warrant a separate question), but you could also use the tikz's calc library to compute points in between the last point and An:

\coordinate (An') at ($(An)!0.30!(A6)$);% 30% along the path from An to A6
\coordinate (A6') at ($(A6)!0.30!(An)$);% 30% along the path from A6 to An

Here I have used points 30% of the way along the path to switch from dotted to dashed.
The color highlighting makes this change more apparent and also makes it more obvious which parts of the code produce what:

I was also thinking along the lines of \Index/\Position but my shortsightedness/inexperience got the better of me. :)
–
hpesoj626Oct 18 '12 at 4:21

@ガベージコレクタ: Was not sure if a dashed or dotted line was required. The default dotted is as above. I think a custom line style is probably called for based on the given image, but that is a different matter and perhaps warrants a separate question if it is desired.
–
Peter GrillOct 18 '12 at 5:05